{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 线性回归"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "算法推导过程中已经给出了求解方法，基于最小二乘法直接求解，但这并不是机器学习的思想，由此引入了梯度下降方法。本次实验课重点讲解其中每一步流程与实验对比分析。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 主要内容：\n",
    "* 线性回归方程实现\n",
    "* 梯度下降效果\n",
    "* 对比不同梯度下降策略\n",
    "* 建模曲线分析\n",
    "* 过拟合与欠拟合\n",
    "* 正则化的作用\n",
    "* 提前停止策略"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import os\n",
    "%matplotlib inline\n",
    "import matplotlib\n",
    "import matplotlib.pyplot as plt\n",
    "plt.rcParams['axes.labelsize'] = 14\n",
    "plt.rcParams['xtick.labelsize'] = 12\n",
    "plt.rcParams['ytick.labelsize'] = 12\n",
    "import warnings\n",
    "warnings.filterwarnings('ignore')\n",
    "np.random.seed(42)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 回归方程：\n",
    "当做是一个巧合就可以了，机器学习中核心的思想是迭代更新"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![title](./img/1.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 303,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "X = 2*np.random.rand(100,1)\n",
    "y = 4+ 3*X +np.random.randn(100,1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 304,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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/KOkvyLq2LgP+tO4nneSz3n4Hpbq7gzoH9vvug+uue+x59u6t56A/KQfEIvt9Ulq/ZqNI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\nvF0llcn3UI8AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(X,y,'b.')\n",
    "plt.xlabel('X_1')\n",
    "plt.ylabel('y')\n",
    "plt.axis([0,2,0,15])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 305,
   "metadata": {
    "collapsed": true,
    "jupyter": {
     "outputs_hidden": true
    }
   },
   "outputs": [],
   "source": [
    "X_b = np.c_[np.ones((100,1)),X]\n",
    "theta_best = np.linalg.inv(X_b.T.dot(X_b)).dot(X_b.T).dot(y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 306,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[4.21509616],\n",
       "       [2.77011339]])"
      ]
     },
     "execution_count": 306,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "theta_best"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 307,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[4.21509616],\n",
       "       [9.75532293]])"
      ]
     },
     "execution_count": 307,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_new = np.array([[0],[2]])\n",
    "X_new_b = np.c_[np.ones((2,1)),X_new]\n",
    "y_predict = X_new_b.dot(theta_best)\n",
    "y_predict"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 308,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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X8Lff7mfMDGmETrYwWqpxaP3GQalvXtNUENKt/j7VcSy88Yav6B99FK6+2p/o++6D666D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\ngIhIQikAiIgk1P8HMLEfwhTZiwMAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(X_new,y_predict,'r--')\n",
    "plt.plot(X,y,'b.')\n",
    "plt.axis([0,2,0,15])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### sklearn api文档：\n",
    "不用背，用到的时候现查完全够用的。\n",
    "https://scikit-learn.org/stable/modules/classes.html"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 309,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[2.77011339]]\n",
      "[4.21509616]\n"
     ]
    }
   ],
   "source": [
    "from sklearn.linear_model import LinearRegression\n",
    "lin_reg = LinearRegression()\n",
    "lin_reg.fit(X,y)\n",
    "print (lin_reg.coef_)\n",
    "print (lin_reg.intercept_)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 梯度下降\n",
    "核心解决方案，不光在线性回归中能用上，还有其他算法中能用上，比如神经网络"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![title](./img/2.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 问题：步长太小"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![title](./img/3.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 问题：步长太大"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![title](./img/4.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![title](./img/5.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "学习率应当尽可能小，随着迭代的进行应当越来越小。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 标准化的作用:\n",
    "- 拿到数据之后基本上都需要做一次标准化操作"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![title](./img/6.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 批量梯度下降计算公式"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![title](./img/7.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 批量梯度下降"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 310,
   "metadata": {
    "collapsed": true,
    "jupyter": {
     "outputs_hidden": true
    }
   },
   "outputs": [],
   "source": [
    "eta = 0.1\n",
    "n_iterations = 1000\n",
    "m = 100\n",
    "theta = np.random.randn(2,1)\n",
    "for iteration in range(n_iterations):\n",
    "    gradients = 2/m* X_b.T.dot(X_b.dot(theta)-y)\n",
    "    theta = theta - eta*gradients"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 311,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[4.21509616],\n",
       "       [2.77011339]])"
      ]
     },
     "execution_count": 311,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "theta"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 312,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[4.21509616],\n",
       "       [9.75532293]])"
      ]
     },
     "execution_count": 312,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_new_b.dot(theta)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 313,
   "metadata": {
    "collapsed": true,
    "jupyter": {
     "outputs_hidden": true
    }
   },
   "outputs": [],
   "source": [
    "theta_path_bgd = []\n",
    "def plot_gradient_descent(theta,eta,theta_path = None):\n",
    "    m = len(X_b)\n",
    "    plt.plot(X,y,'b.')\n",
    "    n_iterations = 1000\n",
    "    for iteration in range(n_iterations):\n",
    "        y_predict = X_new_b.dot(theta)\n",
    "        plt.plot(X_new,y_predict,'b-')\n",
    "        gradients = 2/m* X_b.T.dot(X_b.dot(theta)-y)\n",
    "        theta = theta - eta*gradients\n",
    "        if theta_path is not None:\n",
    "            theta_path.append(theta)\n",
    "    plt.xlabel('X_1')\n",
    "    plt.axis([0,2,0,15])\n",
    "    plt.title('eta = {}'.format(eta))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 314,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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nUyf1dYQTKP/mm/TsTJyovx/vvEOZkSP1MunpjNuqXds9bmvmTAasqxKN+vPE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\nUAgxFOFSUFBQUFBQUAgx/h/bm49jcYNDjwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 720x288 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "theta = np.random.randn(2,1)\n",
    "\n",
    "plt.figure(figsize=(10,4))\n",
    "plt.subplot(131)\n",
    "plot_gradient_descent(theta,eta = 0.02)\n",
    "plt.subplot(132)\n",
    "plot_gradient_descent(theta,eta = 0.1,theta_path=theta_path_bgd)\n",
    "plt.subplot(133)\n",
    "plot_gradient_descent(theta,eta = 0.5)\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 随机梯度下降"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![title](./img/8.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 328,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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Rcc01UmTz5JPwxz/C1VcT3nsoQeqIUiGB35rdcNUv4MILNRjXATlTRi0t8hwl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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "theta_path_sgd=[]\n",
    "m = len(X_b)\n",
    "np.random.seed(42)\n",
    "n_epochs = 50\n",
    "\n",
    "t0 = 5\n",
    "t1 = 50\n",
    "\n",
    "def learning_schedule(t):\n",
    "    return t0/(t1+t)\n",
    "\n",
    "theta = np.random.randn(2,1)\n",
    "\n",
    "for epoch in range(n_epochs):\n",
    "    for i in range(m):\n",
    "        if epoch < 10 and i<10:\n",
    "            y_predict = X_new_b.dot(theta)\n",
    "            plt.plot(X_new,y_predict,'r-')\n",
    "        random_index = np.random.randint(m)\n",
    "        xi = X_b[random_index:random_index+1]\n",
    "        yi = y[random_index:random_index+1]\n",
    "        gradients = 2* xi.T.dot(xi.dot(theta)-yi)\n",
    "        eta = learning_schedule(epoch*m+i)\n",
    "        theta = theta-eta*gradients\n",
    "        theta_path_sgd.append(theta)\n",
    "        \n",
    "plt.plot(X,y,'b.')\n",
    "plt.axis([0,2,0,15])   \n",
    "plt.show()\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### MiniBatch梯度下降"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 342,
   "metadata": {
    "collapsed": true,
    "jupyter": {
     "outputs_hidden": true
    }
   },
   "outputs": [],
   "source": [
    "theta_path_mgd=[]\n",
    "n_epochs = 50\n",
    "minibatch = 16\n",
    "theta = np.random.randn(2,1)\n",
    "t0, t1 = 200, 1000\n",
    "def learning_schedule(t):\n",
    "    return t0 / (t + t1)\n",
    "np.random.seed(42)\n",
    "t = 0\n",
    "for epoch in range(n_epochs):\n",
    "    shuffled_indices = np.random.permutation(m)\n",
    "    X_b_shuffled = X_b[shuffled_indices]\n",
    "    y_shuffled = y[shuffled_indices]\n",
    "    for i in range(0,m,minibatch):\n",
    "        t+=1\n",
    "        xi = X_b_shuffled[i:i+minibatch]\n",
    "        yi = y_shuffled[i:i+minibatch]\n",
    "        gradients = 2/minibatch* xi.T.dot(xi.dot(theta)-yi)\n",
    "        eta = learning_schedule(t)\n",
    "        theta = theta-eta*gradients\n",
    "        theta_path_mgd.append(theta)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 343,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[4.25490684],\n",
       "       [2.80388785]])"
      ]
     },
     "execution_count": 343,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "theta"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true,
    "jupyter": {
     "outputs_hidden": true
    }
   },
   "source": [
    "### 3种策略的对比实验"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 344,
   "metadata": {
    "collapsed": true,
    "jupyter": {
     "outputs_hidden": true
    }
   },
   "outputs": [],
   "source": [
    "theta_path_bgd = np.array(theta_path_bgd)\n",
    "theta_path_sgd = np.array(theta_path_sgd)\n",
    "theta_path_mgd = np.array(theta_path_mgd)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 346,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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YYB1wh9Z6a7XtfgHsAVKAcOAz4N9a6+cq7l8HJDkK4M5IiG56XbrA8eOXvx8/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L2JCcUpqeZVXciSIAlCmSnfDWPY0SZ4pOMkXDvhD3g5YzEe+FJHfz/95ada17xvKXYc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\nRBMRERERWfT/O5U2ncm4lQQAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 864x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(12,6))\n",
    "plt.plot(theta_path_sgd[:,0],theta_path_sgd[:,1],'r-s',linewidth=1,label='SGD')\n",
    "plt.plot(theta_path_mgd[:,0],theta_path_mgd[:,1],'g-+',linewidth=2,label='MINIGD')\n",
    "plt.plot(theta_path_bgd[:,0],theta_path_bgd[:,1],'b-o',linewidth=3,label='BGD')\n",
    "plt.legend(loc='upper left')\n",
    "plt.axis([3.5,4.5,2.0,4.0])\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "实际当中用minibatch比较多，一般情况下选择batch数量应当越大越好。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true,
    "jupyter": {
     "outputs_hidden": true
    }
   },
   "source": [
    "### 多项式回归"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": true,
    "jupyter": {
     "outputs_hidden": true
    }
   },
   "outputs": [],
   "source": [
    "m = 100\n",
    "X = 6*np.random.rand(m,1) - 3\n",
    "y = 0.5*X**2+X+np.random.randn(m,1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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XxZq1vuLCArgIOJOZT6257XHg8uEFI2IfsA9gYWFhNtWNYL3ZU2tXkK7OeJlWVVAuLQ3e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\nUiXDQpJU6f8D6qHL4ctu9CIAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(X,y,'b.')\n",
    "plt.xlabel('X_1')\n",
    "plt.ylabel('y')\n",
    "plt.axis([-3,3,-5,10])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([2.82919615])"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.preprocessing import PolynomialFeatures\n",
    "poly_features = PolynomialFeatures(degree = 2,include_bias = False)\n",
    "X_poly = poly_features.fit_transform(X)\n",
    "X[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([2.82919615, 8.00435083])"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_poly[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "8.004350855174822"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "2.82919615 ** 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[1.10879671 0.53435287]]\n",
      "[-0.03765461]\n"
     ]
    }
   ],
   "source": [
    "from sklearn.linear_model import LinearRegression\n",
    "lin_reg = LinearRegression()\n",
    "lin_reg.fit(X_poly,y)\n",
    "print (lin_reg.coef_)\n",
    "print (lin_reg.intercept_)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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abIlpY0/TqBOlYiSRb4JELuzIye9b6baHCDEnH+SMPaH3XF5/3Swvb+cB6vv3\nN3vvPb+8pCT0Aalqk+rzmJ/vZ/RyrpaZvQLS4Fm7Zs40GzXKrFu3HT31YcN2LF+ypNpMY4nsP6jZ\nxxLZTuXXyLnEfi1JvNHYPXkz2+icewqY7Jy7GOgLjAAOD2ofVQU59kboPZfDD4c334Rvv4U33vC9\nyddeg86d/fLbboPbb/dnRVZc+vXzOf6QT3tP9XkcMMAXloTd66vak167Fq65ZtvCkhJ4/31YtMhX\nwXz5JTzxhF/25JP+9gED/HzBAwdCnz47NtyjR0L7D+o90pBfBEOG+GqlrVv9t9TMmXDuudXvl4kn\noUnIEvkmSPQCdADmAhuBFcA59d0nXXLyNW0zzPldq3nxRbMLLjDr02dHl61FC7PSUr/80UfNpk0z\nmz/frKgo8N1nwuQl+flmrXLLbN+sj+305s9a/mvbet/XX++n8aropbdpYzZ0qB+u18xs48aEth3m\nXLJVt9eQXwTjx/tefNTTRUp6oEnMDBWCig9KRVYlKyuCD8ymTWZvvLHzQdtjjrGdjm526GB2xhk7\nlr/6qllBgdkXX9Sa9smEQG5mPnX1ySf+eTDzE7mfdppZr162tXmLHc/BRx/55c895+cNeOwxsw8+\n8HMKJKGu4BhW4GzIa1FfW9JtwnEJV6JBPrZj1zRUxU/p8nJ/vbw8ghKyli3h0EP9pcKLL8Lnn8N7\n7/m0xIcfQrt2O5aPHQuffOL/b9ECunSBU0+F3/0OgE+uuZ97b2vFF1s7MbdZJ6Y91om8Yzv6dRuD\nmU9VrVsHa9b4dErfvn7Y3cWL/Vlrn3/uD4yuXu3XnzfP5x2+/to/7v33Z3Xf4SzevD9djz2AA7t0\n8ds+4QR/aaC60idhlRLWV2Ja233qShdp6GCpiYJ8FRUflJISH+CzstLkA+OcD9xduvga7qqee84H\n+f/8xwfKFSugQwe/zIxut17Kg2Ul/noJ/mjJmDEwfbp/oAcc4Kt9Ki65uXDaaXDOObBxI1x9tU8K\nZ2XtONvzxBN9yUdREVx1FRQXw6ZNfmCuTZtg4kQ4/XQ/VMQhh/hIWdnDD8Po0T4qLVkCe+zhH1vX\nrn6I6P328+udcgqccsrOFSZ/hVcPDCbg1hUc0y1w1vXloIoYqUksg3wqB58qf1A6dvQH9zLiA9Oj\nR50HEBc9t4pxI76gXWkR380p4qb/KWKf4/f3C0tL4aCDYMMGf1m92n/L/fe/fnlxMcye7ctBy8v9\nF45zsOeeFOwyjLeeKWHM8y/Tom2u/xXSsqWfDCM729+/Sxf/JdG+vf/i6dgRdtttRxA/5BD/66Qe\nYfaqawuOmRY4G/ILQeItduPIZNFvAAAHkElEQVTJN3Y9cSZJ5ssvkXWDfq7r26deW5Edmux48jod\nu3YVvbyKgadSDaZBPteJ7DPTetUi6SB2QT7dcqjpJpFgmmjwDvK5TnSfSkeIJCd2QV69vbolEkwT\nDd7JPNf1pWIqH/DOyvJp+2S3ISLVxS7Ig3p7tSko8EU3FcdD6wrg553n/9Z0VmVliTzXiaZipk6F\nn/zEfwFNnAgHVqqeUT5epGGCnjRE0lRFkLzvPl8YM2ZMzYGy8noPPhjMvhOdKWrtWl+dWfnchGS3\nISI7U5BvIioHybIyX4qe6MHUVCU6U1Rd6zVoOkcRiWe6JpOFlXdONM8exoHrRHP3capXF0kXsauT\nr00mHLQLO++c6HOQCc+VSFPXZOvka5IpB+3CrvFP9IB0kAeu9YUhEq0mEeQz5QSpuNX4Z8qXq0ic\nNYkDr5ly0K4i7zxlSmoBseKM1oKCYNuXLFXEiESvSfTkM+mgXaqpknTqPcftl4lIJmoSQR6azglS\n6ZSayqQvV5G4ajJBvqlIt95zU/lyFUlXCvIxo95zPKgqSYKScpB3zrUA7gaOwk/k/THwSzP7a6rb\nloZR7zmzpdNxFcl8QVTX5ACfAYOB7wCTgMecc90D2LZIk6OqJAlSykHezDaa2Q1mttzMys3sOWAZ\n0D/15omkJl3KSZORKSW/khkCz8k753YD9gPeq2OdscBYgK5duwbdBBEgc9MeOq4iQQo0yDvnmgGz\ngAfNbGlt65nZdGA6+LFrgmyDNI5MODCYTuWkydJxFQlKvUHeOTcfn2+vyetmduS29bKAh4EtwKVB\nNVDST6b0kNOtnFQkCvUGeTMbUt86zjkHzAB2A4abWWnqTZN0lSk9ZKU9RIJL19wD9ASOMrPNAW1T\n0lQ695CrppGU9pCmLog6+W7AOKAE+MJ36gEYZ2azUt2+pJ907SFnShpJpDGlHOTN7FPA1buixEo6\n9pAzJY0k0piaxFDD0jSovlykOo1dI7GRrmkkkSgpyEuspGMaSSRKSteIiMSYgryISIwpyIuIxJiC\nvIhIjCnIi4jEmIK8iEiMKciLiMSYgryISIwpyIuIxJiCvIhIjCnIi4jEmIK8iEiMKciLiMSYgryI\nSIwpyIuIxJiCvIhIjAUe5J1z+zrnip1zjwS9bRERSU4YPflpwJshbFdERJIUaJB3zp0NfA28GuR2\nRUSkYQIL8s65tsBk4PIE1h3rnCt0zhUWFRUF1QQREakiyJ78FGCGmX1W34pmNt3M8swsr1OnTgE2\nQUREKksoyDvn5jvnrJbLAudcX+Ao4PfhNldERJKRk8hKZjakruXOuYlAd2CFcw6gNZDtnDvAzH6Q\nYhtFRKSBEgryCZgOzKl0/Qp80L8koO2LiEgDBBLkzWwTsKniunNuA1BsZjqqKiISoaB68jsxsxvC\n2K6IiCRHwxqIiMSYgryISIwpyIuIxJiCvIhIjCnIi4jEmIK8iEiMKciLiMSYgryISIw5M4u2Ac6t\nBz6ItBHh2hVYE3UjQhLnxwZ6fJku7o9vfzNrU99KoZzxmqQPzCwv6kaExTlXGNfHF+fHBnp8ma4p\nPL5E1lO6RkQkxhTkRURiLB2C/PSoGxCyOD++OD820OPLdHp8pMGBVxERCU869ORFRCQkCvIiIjGm\nIC8iEmNpEeSdc48451Y75751zn3onLs46jYFxTnXwjk3wzn3qXNuvXNukXPu+KjbFSTn3KXOuULn\nXIlz7oGo25Mq51wH59zTzrmN2163c6JuU5Di9npV1kQ+b0nFy3Q4GQrgFuAiMytxzvUA5jvnFpnZ\nW1E3LAA5wGfAYGAFMBx4zDl3oJktj7JhAVoF3AQcC7SMuC1BmAZsAXYD+gLPO+feNrP3om1WYOL2\nelXWFD5vScXLtOjJm9l7ZlZScXXb5XsRNikwZrbRzG4ws+VmVm5mzwHLgP5Rty0oZvaUmc0F1kbd\nllQ551oBpwOTzGyDmS0AngV+HG3LghOn16uqJvJ5SypepkWQB3DO3e2c2wQsBVYDL0TcpFA453YD\n9gPi0iuMm/2ArWb2YaXb3gZ6RdQeSUFcP2/JxMu0CfJmNgFoAwwEngJK6r5H5nHONQNmAQ+a2dKo\n2yM1ag18U+W2b/DvTckgcf68JRMvQw/yzrn5zjmr5bKg8rpmtnXbz+MuwCVhty0IiT4+51wW8DA+\n13tpZA1OUjKvX0xsANpWua0tsD6CtkgDZernLRmJxsvQD7ya2ZAG3C2HDMnJJ/L4nHMOmIE/kDfc\nzErDbldQGvj6ZbIPgRzn3L5m9tG22w4iZj/34yyTP28NVGe8jDxd45zr7Jw72znX2jmX7Zw7FhgF\n/D3qtgXoHqAncJKZbY66MUFzzuU453KBbCDbOZfrnEuXyq2kmNlG/M/fyc65Vs65I4AR+F5hLMTp\n9apFbD9vDYqXZhbpBegE/B/wNfAt8G9gTNTtCvDxdcMf/S7GpwIqLj+Kum0BPsYb2HGUv+JyQ9Tt\nSuHxdADmAhvxZXjnRN0mvV4JP7ZYf94aEi81QJmISIxFnq4REZHwKMiLiMSYgryISIwpyIuIxJiC\nvIhIjCnIi4jEmIK8iEiMKciLiMTY/wMdKrhbPXmiQwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "X_new = np.linspace(-3,3,100).reshape(100,1)\n",
    "X_new_poly = poly_features.transform(X_new)\n",
    "y_new = lin_reg.predict(X_new_poly)\n",
    "plt.plot(X,y,'b.')\n",
    "plt.plot(X_new,y_new,'r--',label='prediction')\n",
    "plt.axis([-3,3,-5,10])\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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m5IzDrz17Fg4c0LpUjBnjluU0K24PkBVFuU1RlP2KohQripKlKEqqu5/hqqhg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nNYIx0CO+C9v95DtiobzvbOZj33r7G/oltoNwR6Bpr1vBQKxbrRxrxxHeSh0qh4x8DSCnJJLC+Q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\nhUTacsoj8gAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 864x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.pipeline import Pipeline\n",
    "from sklearn.preprocessing import StandardScaler\n",
    "plt.figure(figsize=(12,6))\n",
    "for style,width,degree in (('g-',1,100),('b--',1,2),('r-+',1,1)):\n",
    "    poly_features = PolynomialFeatures(degree = degree,include_bias = False)\n",
    "    std = StandardScaler()\n",
    "    lin_reg = LinearRegression()\n",
    "    polynomial_reg = Pipeline([('poly_features',poly_features),\n",
    "             ('StandardScaler',std),\n",
    "             ('lin_reg',lin_reg)])\n",
    "    polynomial_reg.fit(X,y)\n",
    "    y_new_2 = polynomial_reg.predict(X_new)\n",
    "    plt.plot(X_new,y_new_2,style,label = 'degree   '+str(degree),linewidth = width)\n",
    "plt.plot(X,y,'b.')\n",
    "plt.axis([-3,3,-5,10])\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "特征变换的越复杂，得到的结果过拟合风险越高，不建议做的特别复杂。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 数据样本数量对结果的影响"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {
    "collapsed": true,
    "jupyter": {
     "outputs_hidden": true
    }
   },
   "outputs": [],
   "source": [
    "from sklearn.metrics import mean_squared_error\n",
    "from sklearn.model_selection import train_test_split\n",
    "\n",
    "def plot_learning_curves(model,X,y):\n",
    "    X_train, X_val, y_train, y_val = train_test_split(X,y,test_size = 0.2,random_state=100)\n",
    "    train_errors,val_errors = [],[]\n",
    "    for m in range(1,len(X_train)):\n",
    "        model.fit(X_train[:m],y_train[:m])\n",
    "        y_train_predict = model.predict(X_train[:m])\n",
    "        y_val_predict = model.predict(X_val)\n",
    "        train_errors.append(mean_squared_error(y_train[:m],y_train_predict[:m]))\n",
    "        val_errors.append(mean_squared_error(y_val,y_val_predict))\n",
    "    plt.plot(np.sqrt(train_errors),'r-+',linewidth = 2,label = 'train_error')\n",
    "    plt.plot(np.sqrt(val_errors),'b-',linewidth = 3,label = 'val_error')\n",
    "    plt.xlabel('Trainsing set size')\n",
    "    plt.ylabel('RMSE')\n",
    "    plt.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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qkCGqffsmvt8mTewAHpo/6CA7a4+1X1D96U8T2+4RR4T/psl+J1dcYY+RJxZg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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "lin_reg = LinearRegression()\n",
    "plot_learning_curves(lin_reg,X,y)\n",
    "plt.axis([0,80,0,3.3])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "数据量越少，训练集的效果会越好，但是实际测试效果很一般。实际做模型的时候需要参考测试集和验证集的效果。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 多项式回归的过拟合风险"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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R/I2NHWsveU93NIs0h7Fjw7ftkSNDuSIh9O8ffj77bLhRasGCUF69GpYtg4UL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\nh/my7LbeBxYAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "polynomial_reg = Pipeline([('poly_features',PolynomialFeatures(degree = 25,include_bias = False)),\n",
    "             ('lin_reg',LinearRegression())])\n",
    "plot_learning_curves(polynomial_reg,X,y)\n",
    "plt.axis([0,80,0,5])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "越复杂越过拟合"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 正则化"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "对权重参数进行惩罚，让权重参数尽可能平滑一些，有两种不同的方法来进行正则化惩罚:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![title](./img/9.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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EdLbK73Z+9CjUru3KyUZGejsqETkTGRmuBUL37rD2qWe5Jhk6HvWnll/tEvv2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\n",
      "text/plain": [
       "<Figure size 1008x432 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# L2 正则化\n",
    "# 损失函数中加入一个正则化项来减少模型的复杂度，从而防止过拟合。这种正则化项是模型参数的平方和乘以一个正则化系数（通常标记为 λ 或 α）。Ridge 回归也被称为 L2 正则化\n",
    "from sklearn.linear_model import Ridge\n",
    "np.random.seed(42)\n",
    "m = 20\n",
    "X = 3*np.random.rand(m,1)\n",
    "y = 0.5 * X +np.random.randn(m,1)/1.5 +1\n",
    "X_new = np.linspace(0,3,100).reshape(100,1)\n",
    "\n",
    "def plot_model(model_calss,polynomial,alphas,**model_kargs):\n",
    "    for alpha,style in zip(alphas,('b-','g--','r:')):\n",
    "        model = model_calss(alpha,**model_kargs)\n",
    "        if polynomial:\n",
    "            model = Pipeline([('poly_features',PolynomialFeatures(degree =10,include_bias = False)),\n",
    "             ('StandardScaler',StandardScaler()),\n",
    "             ('lin_reg',model)])\n",
    "        model.fit(X,y)\n",
    "        y_new_regul = model.predict(X_new)\n",
    "        lw = 2 if alpha > 0 else 1\n",
    "        plt.plot(X_new,y_new_regul,style,linewidth = lw,label = 'alpha = {}'.format(alpha))\n",
    "    plt.plot(X,y,'b.',linewidth =3)\n",
    "    plt.legend()\n",
    "\n",
    "plt.figure(figsize=(14,6))\n",
    "plt.subplot(121)\n",
    "plot_model(Ridge,polynomial=False,alphas = (0,10,100))\n",
    "plt.subplot(122)\n",
    "plot_model(Ridge,polynomial=True,alphas = (0,10**-5,1))\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "惩罚力度越大，alpha值越大的时候，得到的决策方程越平稳。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true,
    "jupyter": {
     "outputs_hidden": true
    }
   },
   "source": [
    "![title](./img/10.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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i4ggICCAsLIyMjIyL2pkLepXyv/b3d5YA8vX1JTs7G4AJEybQt29f5s6dy44dOwgroKpN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\nQmCC\n",
      "text/plain": [
       "<Figure size 1008x432 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# L1 正则化\n",
    "\n",
    "from sklearn.linear_model import Lasso\n",
    "\n",
    "plt.figure(figsize=(14,6))\n",
    "plt.subplot(121)\n",
    "plot_model(Lasso,polynomial=False,alphas = (0,0.1,1))\n",
    "plt.subplot(122)\n",
    "plot_model(Lasso,polynomial=True,alphas = (0,10**-1,1))\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true,
    "jupyter": {
     "outputs_hidden": true
    }
   },
   "source": [
    "多做实验，得出结果！！！"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true,
    "jupyter": {
     "outputs_hidden": true
    }
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.10"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}
